A counterexample to the Hirsch conjecture

@article{Santos2010ACT,
  title={A counterexample to the Hirsch conjecture},
  author={Francisco Santos},
  journal={ArXiv},
  year={2010},
  volume={abs/1006.2814}
}
  • F. Santos
  • Published 2010
  • Computer Science, Mathematics
  • ArXiv
The Hirsch Conjecture (1957) stated that the graph of a d-dimensional polytope with n facets cannot have (combinatorial) diameter greater than n d. That is, any two vertices of the polytope can be connected by a path of at most n d edges. This paper presents the rst counterexample to the conjecture. Our polytope has dimension 43 and 86 facets. It is obtained from a 5-dimensional polytope with 48 facets that violates a certain generalization of the d-step conjecture of Klee and Walkup. 
Recent progress on the combinatorial diameter of polyhedra and simplicial complexes
  • F. Santos
  • Computer Science, Mathematics
  • SoCG '13
  • 2013
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TLDR
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  • M. Todd
  • Mathematics, Computer Science
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